Question: Which decimal is equivalent to $\dfrac{4}{15}$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $0.26$ (Choice B) B $0.2626$ (Choice C) C $0.\overline{26}$ (Choice D) D $0.2\overline{6}$
$ \dfrac{4}{15}$ represents $4 \div 15$. ${1}$ ${5}$ ${4}$ ${0}$ ${0}$ ${.}$ ${.}$ $\text{Write in a decimal and a zero.}$ ${1}$ ${5}$ ${4}$ ${0}$ ${0}$ ${.}$ ${.}$ $\text{Write in a decimal and a zero.}$ $\text{How many times does }15\text{ go into }{40}\text{?}$ ${2}$ ${3}$ ${0}$ $-$ ${1}$ ${0}$ ${40}\div15={2}\text{ with a remainder of }{10}$ $\text{How many times does }15\text{ go into }{100}\text{?}$ ${0}$ ${0}$ ${6}$ ${9}$ ${0}$ $-$ ${1}$ ${0}$ ${100}\div15={6}\text{ with a remainder of }{10}$ $\text{How many times does }15\text{ go into }{100}\text{?}$ ${0}$ ${0}$ ${6}$ ${9}$ ${0}$ $-$ ${1}$ ${0}$ ${100}\div15={6}\text{ with a remainder of }{10}$ $\text{How many times does }15\text{ go into }{100}\text{?}$ ${0}$ ${0}$ ${6}$ ${6}$ ${9}$ ${0}$ $-$ ${1}$ ${0}$ ${1}$ ${0}$ ${100}\div15={6}\text{ with a remainder of }{10}$ Notice how the decimal is repeating and will continue to repeat as we bring down more zeros. So $\dfrac{4}{15}$ is equivalent to $0.2\overline{6}$.